There is one routine on the calculator, called 1-Variable Statistics which will find

- the sample mean
- the sum of the data values
- the sum of the squares of the data values
- the sample standard deviation
- the population standard deviation
- the sample size
- the minimum value
- the first quartile
- the median
- the third quartile
- the maximum value

It also saves all of these values to variables so they can be used in other calculations without having to re-enter the information.

- Enter the data. If the raw data is used, it goes into one list only. If a frequency distribution is to be entered, then put the data values into one list and the corresponding frequency into another list.
- Calculate the 1-Variable Statistics (
`STATS CALC 1`) - Be sure to specify which list your data is in when you do the 1-Variable Statistics.

- 1-VAR STATS L
_{1} - This will find the 1-Variable statistics for the data contained in list 1. Each element in list 1 is assumed to have a frequency of 1.
- 1-VAR STATS L
_{1},L_{2} - This will find the 1-Variable statistics for the data contained in list 1. Each element in list 1 is assumed to have a frequency of the corresponding element in list 2.

The results of the 1-Variable Statistics (and any other statistical calculations
done later) are under the VARS key, menu choice number 5: STATISTICS. Go ahead
and press that now "`VARS 5`"

Since the calculator gives the standard deviations instead of the variances, the first thing often found is the variance. The sample standard deviation is number 3 and the population standard deviation is number 4.

VARS 5 3 x^{2}- sample variance VARS 5 4 x^{2}- population variance

The variation is used as a step in finding the variance and ultimately the standard deviation when calculating those values by hand. Since we are going to concentrate on understanding the statistics and letting the calculator concentrate on finding the statistics, we aren't going to use the variation very often.

One place that the variation will come into use is when we're working with Analysis of Variance (ANOVA). The total variation can be found by multiplying the degrees of freedom by the sample variance or the sample size by the population variance.

( VARS 5 1 - 1 ) * VARS 5 3 x^{2}VARS 5 1 * VARS 5 4 x^{2}

The way to compute the z-score is to subtract the mean from each value and then divide by the standard deviation. Since the mean and standard deviation are stored in variables, you can use them in the formula directly. This expression will convert the entire list at once. If you wish to find the z-score for a single value, then replace the L1 with that value.

( L1 -Xbar) /Sx

To generate the *Xbar*, press: ` VARS 5 2`

To generate the *Sx*, press:` VARS 5 3`

The quartiles are stored under `VARS STATISTICS(5) BOX`.

Q3 - Q1

or

VARS 5 BOX 3 - VARS 5 BOX 1

MAXX - MINX

or

VARS 5 9 - VARS 5 8

( MAXX + MINX ) / 2

or

( VARS 5 9 - VARS 5 8 ) / 2

Q1 - 1.5 * (Q3 - Q1)

and

Q3 + 1.5 * (Q3 - Q1)

Q1 - 3 * (Q3 - Q1)

and

Q3 + 3 * (Q3 - Q1)